Question

6. What is area of the largest triangle that can be inscribed in a semi-circle of radius units.​

Answer 1

The area of a triangle is equal to the base times the height.

In a semi circle, the diameter is the base of the semi-circle.

This is equal to 2×r (r = the radius)

If the triangle is an isosceles triangle with an angle of 45° at each end, then the height of the triangle is also a radius of the circle.

A = ½×b×h formula for the area of a triangle becomes

A = ½ ×2×r×r because:

The base of the triangle is equal to 2×r

The height of the triangle is equal to r

A = ½ ×2×r×r becomes:

A = r²